Some properties of hyper-dual and bicomplex numbers with Leonardo number components

This thesis consists of five chapters. The first chapter is mentioned to introduction of thesis. In the second part, we mentioned the basic definitions and concepts necessary to better understand the hyper dual Leonardo numbers structure and bicomplex Leonardo numbers. In the third chapter, hyper dual Leonardo numbers, which is one of the original parts of the thesis, are defined and for hyper dual Leonardo numbers, the recurrence relation, Binet's like formula, sum formulas, Catalan's identity, Cassini's identity, D'ocagne's identity are obtained. In the fourth chapter, bicomplex Leonardo numbers, which is another original part of the thesis, is defined and the Binet's like formula, sum formulas, Catalan's identity, Cassini's identity, D'ocagne's identity and some important identity are obtained for bicomplex Leonardo numbers. The last part is mentioned for results, discussions and suggestions.